As my eye hops back and forth between the two rapidly changing numbers, it looks like they're always *different*... unless I focus on a point between them, so I can't clearly see either, but can roughly tell that they look the same.
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When I was making my u-sub animation a while ago, i was thinking about something similar.. how even an innocent non-linear u-sub seems to deform the region in a way that’s not obviously equal in area to its ‘parent’ region so i was wondering if there were .. 1/2
ways to quantify the notion of ‘intuitive’ equal area .. started by fixing 2 points in the x-axis then started deforming curves connecting them .. it started to smell like topology so i dropped it and went back to research
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Maybe deform one curve into the other along a geodesic defined by the earth move distance, which preserves the integral
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hmm.. i think I understand .. so if I have a curve γ(t) on some manifold, then moving along a geodesic to some γ’(t) will have equal area?
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There’s a section in my novella “Phoresis” where someone needs to convince potential backers that the weight of an *extremely* tall tower will be bounded because of the inverse square law, and they decide to do it by pouring liquid between suitably shaped tanks.
Thanks. Twitter will use this to make your timeline better. UndoUndo
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